Nonsolvable groups with five character codegrees

Liu, Yang; Yang, Yong

doi:10.1080/00927872.2020.1832106

Cited by 11 publications

(5 citation statements)

References 14 publications

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“…In this paper, we study a different set of integers related to a finite group G. We define the codegree of a character χ to be codeg(χ) = |G : ker χ|/χ(1). In [9], the concept of codegree was introduced and various properties of the codegree have been studied in [3,[6][7][8][9]12].…”

Section: Introductionmentioning

confidence: 99%

On Analogues of Huppert’s Conjecture

Yang

2021

Bull. Aust. Math. Soc.

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Let G be a finite group and $\chi $ be a character of G. The codegree of $\chi $ is $\text{codeg} (\chi ) ={|G: \ker \chi |}/{\chi (1)}$ . We write $\pi (G)$ for the set of prime divisors of $|G|$ , $\pi (\text{codeg} (\chi ))$ for the set of prime divisors of $\text{codeg} (\chi )$ and $\sigma (\text{codeg} (G))= \max \{|\pi (\text{codeg} (\chi ))| : \chi \in {\textrm {Irr}}(G)\}$ . We show that $|\pi (G)| \leq ({23}/{3}) \sigma (\text{codeg} (G))$ . This improves the main result of Yang and Qian [‘The analog of Huppert's conjecture on character codegrees’, J. Algebra478 (2017), 215–219].

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Section: Introductionmentioning

confidence: 99%

On Analogues of Huppert’s Conjecture

Yang

2021

Bull. Aust. Math. Soc.

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“…The definition was modified to cod( χ) = |G : ker( χ)|/χ(1) by Qian et al in [18] so that there is no different meaning for cod( χ) when χ is considered as a character in some quotient group of G. Because the relationship between codegrees and degrees is very close, we may expect to characterise the structure of groups by codegrees. During the past few years, the study of character codegrees has been very active and many results have been obtained, including the relationship between codegrees and element orders, codegrees of p-groups and groups with few codegrees (see, for example, [2,8,11,14,15,17]).…”

Section: Introductionmentioning

confidence: 99%

“…Because the relationship between codegrees and degrees is very close, we may expect to characterise the structure of groups by codegrees. During the past few years, the study of character codegrees has been very active and many results have been obtained, including the relationship between codegrees and element orders, codegrees of p -groups and groups with few codegrees (see, for example, [2, 8, 11, 14, 15, 17]).…”

Section: Introductionmentioning

confidence: 99%

Recognising Ree Groups Using the Codegree Set

Guan

ZHANG²,

Yang

2022

Bull. Aust. Math. Soc.

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“…In [12], we have obtained many basic properties of codegree and also studied its related prime graph. Since then, this new definition of codegree has attracted quite amount of interest [1, 5, 8–11, 13, 14]. Among those, the most interesting finding perhaps is the relation between the character codegrees and the element orders [8, 11].…”

Section: Introductionmentioning

confidence: 99%